Key Excursion

[william ballard]

Why, Jon, I thought you'd never ask......

On Apr 15, 2006, at 12:15 AM, Jon Page wrote:
> Has there ever been established an arc in which the key optimally  
> rotates?

As far as mechanical efficiency, the only thing you have to remember  
is that while the motion of all these pivoting parts is angular,  
angular motion introduces a kind of inefficiency which we wouldn't  
have to have if the motion were purely linear. (Imagine the hammer  
mounted on the end of a piston. Yea, I know it's hard, and that's the  
reason the hammer gets delivered or pivoting levers).

The inefficiency enters when the radius of the pivoting moves away  
from normal (perpendicular) to the direction you want the payload to go.

Say (in a grand action), we want the hammer to move vertically from  
the rest point to the strike point, and the key is the first of three  
pivoting arms in that lever train. The back lever arm of the key  
(from the fulcrum to the top of the capstan) will move in an angular  
fashion,

That angular motion will break down into horiztontal and vertical  
vectors. It's the vertical vector we want because that's the one  
lifting the repetition. The horizontal is simply sliding, but it's  
worse than wasted: it's pure friction.

At the moment when that lever arm is horizontal,the vertical vector  
will be 100% and the horizontal, 0%. Optimum efficiency, right? The  
further that lever arm swings upwards from perpendicular to the  
desired motion, the more the more the horizontal vector picks up at  
the expense of the vertical vector.

What an extreme example of action inefficiency? How 'bout a vertical  
action with wood dowels on tall wires.

This should answer the question from the standpoint of action  
efficiency. As we all know the back half of the key lever never gets  
much below 20º above dead level, and the short arm of the hammer  
shank is far worse.

Usually the matter of inclination is settled by how well the keyboard  
is going to fit within the case parts, and these ideal of efficiency  
of angular motion are left behind in the dust.

> Does key length factor in, either vertical or grand. Is there an  
> association between touchweight measurements and dynamic playing.

Length actually increases this efficiency, although inducing another  
in the form of flexing keys.

> Just curious as to opinions. I have mine of course.
I thought it was a rhetorical question. (I have mine too).

Mr. Bill

"I go, two plus like, three is pretty much totally five. Whatever"
     ...........The new math
+++++++++++++++++++++